wheagy,
Thank you.
Yes, the DS1307 RTC is the way to go IMO. Especially with a battery B/U. However you will need to squeeze out 2 more pins - analog 4&5 - for the I2C.
Beyond that, you will likely need code to display and scroll the time on the matrix. Mine is tied to LedControl & characters in EEPROM, but I would be happy to post it if you think it would be useful.
Something you could do is make your own shield that holds the DS1307, battery, and what ever else. If you want the schematics I could post them or PM them.